Component selection

Some components are already available at the workplace, including IGBT modules, di-ode bridge, fuses, didi-odes, cables, PLC units and switching devices. The IGBT modules include their own drivers and are rated up to 1200 V in terms of collector-to-emitter voltage. All components are dimensioned to withstand the current and voltage limits.

Only the passive components need to be chosen.

According to the inductor volt-second balance or, rather, the average inductor-voltage over one period must be zero [7]. During on-time, voltage over inductor is equal to Uin - Uo while at off-times the voltage is –Uo, if ESRs are neglected.

∫ 𝑈_𝑖𝑛− 𝑈_𝑜𝑑𝑡

Where Uo is the output voltage, Uin the input voltage and D the duty ratio at steady state.

Eq. 5.1 means that the duty ratio D is equal to the ratio of output voltage and input volt-age which, in general, should be the relationship. As D is known, other parameters are known to solve a suitable inductor size as follows in Eq. 5.2.

𝑣_𝐿 = 𝐿^{𝑑𝑖𝐿−𝑝𝑝}

𝑑𝑡 (5.2)

Where vL is the inductor voltage, L the inductor value and ΔiL-pp stands for the peak-to-peak inductor current ripple. The inductor size can be solved either using on- or off-time as shown below in Eq. 5.3 and 5.4. voltage 5.3 to equation 5.2. Eq. 5.6 is the same as Eq. 5.5, only the solved quantity is changed.

𝐿 =^{𝐷𝑇𝑠(𝑉𝑖𝑛−𝑉𝑜)}

𝛥𝑖_{𝑙−𝑝𝑝} (5.5)

𝛥𝑖_{𝑙−𝑝𝑝} = ^{𝐷𝑇𝑠(𝑉𝑖𝑛−𝑉𝑜)}

𝐿 (5.6)

Differentiating Eq. 5.6 with respect to Vo and solving the derivative yields Eq. 5.7.

𝛥𝑖_{𝑙−𝑝𝑝} = 𝑉_𝑖𝑛− 𝑉_𝑜

𝐷 = (50 mΩ + 10 mΩ) · 60 A + 120 V + 2 V 170 V − (1 mΩ − 10 mΩ) · 60 A + 2 V

𝐷 = 0.7279

L size can be calculated by Eq. 5.5. The allowable ripple is assumed to be 10 %.

𝐿 = 170 𝑉 − 120 𝑉

60 𝐴 · 10 % · 0.7279 · 1 5 𝑘𝐻𝑧 𝐿 = 1.2 𝑚𝐻

If the current ripple would be 5 %, the inductor size would be 2.4 mH. However, 1.2 mH is adequate in this application since it guarantees small ripple and it is smaller and cheaper compared to an inductor which is 2.4 mH. This inductor is shown in Figure 6 as the inductor of the buck converter. The current ripple in the situation of the maximum charging current 600 A is:

𝛥𝑖_{𝑙−𝑝𝑝} =170 𝑉 − 120 𝑉

1.2 𝑚𝐻 · 0.89 · 1

5 𝑘𝐻𝑧= 7.4 𝐴

The inductor should not saturate under the maximum load current, otherwise it is not usable. Furthermore, a low value for ESR is desired to avoid induced voltage drops [26].

Inductors tend suffer a reduction in inductance as current increases, eventually up to a point where the inductor has no inductance at all. This is the saturation of an inductor.

In EMI-perspective, the best alternative is to use an inductor which has a closed mag-netic circuit [27], such as toroids. If an inductor with an air gap is used stray fields will be larger, but the saturation does not happen so easily.

Ferrites could be used for low-pass filtering [26], since at high frequencies ferrites be-come resistive and can filter the high frequency components of the signal. At low fre-quencies ferrites behave similarly compared to inductors. Ferrites can be understood as inductors at low frequencies and as a combination of a resistor and an inductor at high frequencies. There are manufacturers who produce round-cable ferrites, such as [28], but the current ratings are not available.

Capacitors have different operating frequencies depending on the type of the capacitor.

If required operating frequency is in the range of kilohertz, aluminium electrolytic

ca-pacitors are a good choice since these caca-pacitors can be used in a wide range of voltage rates and sizes. The voltage range is up to 500 V and one of their qualities is a high ca-pacitance-to-volume ratio. A minor drawback is that they are polarized, i.e. cannot tol-erate reverse voltages. Considering their operation, capacitors have equivalent series re-sistance (ESR) as well as equivalent series inductance (ESL) which means no capacitor is purely capacitive. [29]

As was mentioned ESR is one of capacitors’ parameter. The larger size a capacitor has, the smaller is the ESR value of the capacitor. So, to give some perspective, an alumini-um capacitor, which has a size of 100 μF, has ESR value of 377 mΩ. In comparison a capacitor of 1200 μF has ESR value of only 75 mΩ [30]. The capacitor size is deter-mined by Eq. 5.8. In this the voltage ripple can be 5 %. charged with current of 600 A, the capacitor size is:

𝐶 =7.4 𝐴 · 1 5000 𝐻𝑧

8 · 5 % · 120 𝑉 = 31 𝜇𝐹 With 2 % voltage ripple:

𝐶 =7.4 𝐴 · 1 5000 𝐻𝑧

8 · 2 % · 120 𝑉 = 77 𝜇𝐹

With some safety margin an electrolytic capacitor of 100 μF is chosen for the output ca-pacitor since the frequency is low. The ESL of the caca-pacitors should be low to avoid self-resonance. Furthermore, the voltage rating should be high enough to match the re-quirements set by the output current and voltage.

The input capacitor value can be determined by simulating or by calculating. In this case, simulating is utilized and below are illustrated waveforms with following capaci-tances: 100 μF and 0.01 F (Figure 20 and Figure 21). In these simulations a buck

con-Figure 20. Input voltage ripple, C = 100 μF and Rc = 0.377 Ω.

Figure 21. Input voltage ripple, C = 0.01 F and Rc = 0.004 Ω.

Based on the simulations, it seems that to reduce the ripple, the input capacitor must be at least millimetre farads. The 100 µF input capacitor provides a ripple voltage of al-most 30 V, while the 10 mF capacitor decreases the peak-to-peak ripple to 19 V. How-ever, with accurate control the input voltage ripple is not that important. The input ca-pacitor can be larger to avoid ripple and improve quality of the load current, but it

should have a pre-load circuit to avoid high start transient current. In this case a capaci-tor of 1 mF could be used.

All component values are known and are shown in Table 1. Some of the parameters are estimated values, but others are known values and taken from the datasheets which are shown in references. The battery estimated impedance 4 mΩ is given for one battery and the total impedance for 5 batteries in series is equal to 20 mΩ.

Table 1. Initial buck parameters.

Inductor size, L 1.2 mH Diode voltage, Vd 2 V

Equivalent series resistance, rL 50 mΩ Input voltage, Vin 170 V

Capacitance, C 100 μF Output voltage, Vo 120 V

Equivalent series resistance, rC 20 mΩ Output current, Io 50 - 600 A Switch resistance, rsw 1mΩ Switching frequency, fs 5 kHz

Diode resistance, rd 10 mΩ Period, Ts 0.2 ms

Battery impedance, rs 4 mΩ Total battery impedance, rs-tot 20 mΩ

Simulations are done tuning controllers for output current of 300 A, and the total open circuit of voltage of 5 batteries in series is assumed to be 120 V or 24 V·5. The equiva-lent series resistances rC and rL are directional values, not necessary the exact values.

The input voltage is 170 V to gain allowable duty ratios, otherwise the switch would be 100 % closed for some periods.